The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  1 X^3  1  1  X  1  1 X^2+X  1  1 X^2+X  1  1  0 X^3+X^2  X X^2 X^3+X  1  1 X^2+X  1  1  1  1  1  1 X^2+X X^3  1  1 X^2 X^3+X  1  1  1  1  1  1  X  1  1 X^3+X^2 X^3+X X^2  0  1  1  1  1  0  1  1 X^3+X X^2+X  1  1  1  1  1  X  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3 X^2+X+1  1 X^3+X^2 X+1  1  X X^3+1  1 X^2 X^3+X^2+1  1  1 X^2+X  1 X^3+X^2+X+1 X^3+X  1  1  1  1  1  0 X+1  1 X^3+X^2+X  1 X^3+X^2 X^3+X^2+X+1  X X^3+X^2+1  1  1 X^2+X X^3+1  1  1 X^3  0 X^3+X X^3+X+1 X+1 X^2+1 X^3+X^2 X^3+X^2 X^3+X^2+X  1  1  X  1 X^2+1 X^2+X X^3+1 X+1  1 X^3+X^2 X^3+X+1  1  1 X^2+1 X^3+X^2+X  1 X^3+X^2+X+1  1  1 X^2  X  0
 0  0 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3  0 X^2 X^2 X^3 X^3 X^3  0 X^3+X^2 X^2  0  0 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0  0  0 X^3+X^2  0 X^3  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+146x^70+172x^71+369x^72+216x^73+316x^74+224x^75+275x^76+136x^77+130x^78+20x^79+37x^80+1x^84+2x^88+3x^96

The gray image is a linear code over GF(2) with n=592, k=11 and d=280.
This code was found by Heurico 1.16 in 0.453 seconds.